AMC 12B 2009 Problem 8

When a bucket is two-thirds full of water, the bucket and water weigh a kilograms. When the bucket is one-half full of water the total weight is b kilograms. In terms of a and b, what is the total weight in kilograms when the bucket is full of water?

Answer Choices
A. \dfrac{2}{3} a+\dfrac{1}{3} b
B. \dfrac{3}{2} a-\dfrac{1}{2} b
C. \dfrac{3}{2} a+b
D. \dfrac{3}{2} a+2 b
E. 3 a-2 b